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Commons Math example source code file (PoissonDistributionTest.java)

This example Commons Math source code file (PoissonDistributionTest.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

default_test_poisson_parameter, exception, exception, integerdistributionabstracttest, mathexception, nan, override, override, poissondistribution, poissondistribution, poissondistributionimpl, poissondistributionimpl, poissondistributiontest, zero

The Commons Math PoissonDistributionTest.java source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math.distribution;

import org.apache.commons.math.MathException;

/**
 * <code>PoissonDistributionTest
 *
 * @version $Revision: 924345 $ $Date: 2010-03-17 12:03:56 -0400 (Wed, 17 Mar 2010) $
 */
public class PoissonDistributionTest extends IntegerDistributionAbstractTest {

    /**
     * Poisson parameter value for the test distribution.
     */
    private static final double DEFAULT_TEST_POISSON_PARAMETER = 4.0;

    /**
     * Constructor.
     * @param name
     */
    public PoissonDistributionTest(String name) {
        super(name);
        setTolerance(1e-12);
    }

    /**
     * Creates the default discrete distribution instance to use in tests.
     */
    @Override
    public IntegerDistribution makeDistribution() {
        return new PoissonDistributionImpl(DEFAULT_TEST_POISSON_PARAMETER);
    }

    /**
     * Creates the default probability density test input values.
     */
    @Override
    public int[] makeDensityTestPoints() {
        return new int[] { -1, 0, 1, 2, 3, 4, 5, 10, 20};
    }

    /**
     * Creates the default probability density test expected values.
     * These and all other test values are generated by R, version 1.8.1
     */
    @Override
    public double[] makeDensityTestValues() {
        return new double[] { 0d, 0.0183156388887d,  0.073262555555d,
                0.14652511111d, 0.195366814813d, 0.195366814813,
                0.156293451851d, 0.00529247667642d, 8.27746364655e-09};
    }

    /**
     * Creates the default cumulative probability density test input values.
     */
    @Override
    public int[] makeCumulativeTestPoints() {
        return new int[] { -1, 0, 1, 2, 3, 4, 5, 10, 20 };
    }

    /**
     * Creates the default cumulative probability density test expected values.
     */
    @Override
    public double[] makeCumulativeTestValues() {
        return new double[] { 0d,  0.0183156388887d, 0.0915781944437d,
                0.238103305554d, 0.433470120367d, 0.62883693518,
                0.78513038703d,  0.99716023388d, 0.999999998077 };
    }

    /**
     * Creates the default inverse cumulative probability test input values.
     * Increased 3rd and 7th values slightly as computed cumulative
     * probabilities for corresponding values exceeds the target value (still
     * within tolerance).
     */
    @Override
    public double[] makeInverseCumulativeTestPoints() {
        return new double[] { 0d,  0.018315638889d, 0.0915781944437d,
                0.238103305554d, 0.433470120367d, 0.62883693518,
                0.78513038704d,  0.99716023388d, 0.999999998077 };
    }

    /**
     * Creates the default inverse cumulative probability density test expected values.
     */
    @Override
    public int[] makeInverseCumulativeTestValues() {
        return new int[] { -1, 0, 1, 2, 3, 4, 5, 10, 20};
    }

    /**
     * Test the normal approximation of the Poisson distribution by
     * calculating P(90 ? X ? 110) for X = Po(100) and
     * P(9900 ? X ? 10200) for X  = Po(10000)
     */
    public void testNormalApproximateProbability() throws Exception {
        PoissonDistribution dist = new PoissonDistributionImpl(100);
        double result = dist.normalApproximateProbability(110)
                - dist.normalApproximateProbability(89);
        assertEquals(0.706281887248, result, 1E-10);
        dist.setMean(10000);
        result = dist.normalApproximateProbability(10200)
        - dist.normalApproximateProbability(9899);
        assertEquals(0.820070051552, result, 1E-10);
    }

    /**
     * Test the degenerate cases of a 0.0 and 1.0 inverse cumulative probability.
     * @throws Exception
     */
    public void testDegenerateInverseCumulativeProbability() throws Exception {
        PoissonDistribution dist = new PoissonDistributionImpl(DEFAULT_TEST_POISSON_PARAMETER);
        assertEquals(Integer.MAX_VALUE, dist.inverseCumulativeProbability(1.0d));
        assertEquals(-1, dist.inverseCumulativeProbability(0d));
    }

    public void testMean() {
        PoissonDistribution dist = new PoissonDistributionImpl(DEFAULT_TEST_POISSON_PARAMETER);
        try {
            dist.setMean(-1);
            fail("negative mean.  IllegalArgumentException expected");
        } catch(IllegalArgumentException ex) {
        }

        dist.setMean(10.0);
        assertEquals(10.0, dist.getMean(), 0.0);
    }

    public void testLargeMeanCumulativeProbability() {
        PoissonDistribution dist = new PoissonDistributionImpl(1.0);
        double mean = 1.0;
        while (mean <= 10000000.0) {
            dist.setMean(mean);

            double x = mean * 2.0;
            double dx = x / 10.0;
            double p = Double.NaN;
            double sigma = Math.sqrt(mean);
            while (x >= 0) {
                try {
                    p = dist.cumulativeProbability(x);
                    assertFalse("NaN cumulative probability returned for mean = " +
                            mean + " x = " + x,Double.isNaN(p));
                    if (x > mean - 2 * sigma) {
                        assertTrue("Zero cum probaility returned for mean = " +
                                mean + " x = " + x, p > 0);
                    }
                } catch (MathException ex) {
                    fail("mean of " + mean + " and x of " + x + " caused " + ex.getMessage());
                }
                x -= dx;
            }

            mean *= 10.0;
        }
    }

    /**
     * JIRA: MATH-282
     */
    public void testCumulativeProbabilitySpecial() throws Exception {
        PoissonDistribution dist = new PoissonDistributionImpl(1.0);
        dist.setMean(9120);
        checkProbability(dist, 9075);
        checkProbability(dist, 9102);
        dist.setMean(5058);
        checkProbability(dist, 5044);
        dist.setMean(6986);
        checkProbability(dist, 6950);
    }

    private void checkProbability(PoissonDistribution dist, double x) throws Exception {
        double p = dist.cumulativeProbability(x);
        assertFalse("NaN cumulative probability returned for mean = " +
                dist.getMean() + " x = " + x, Double.isNaN(p));
        assertTrue("Zero cum probability returned for mean = " +
                dist.getMean() + " x = " + x, p > 0);
    }

    public void testLargeMeanInverseCumulativeProbability() throws Exception {
        PoissonDistribution dist = new PoissonDistributionImpl(1.0);
        double mean = 1.0;
        while (mean <= 100000.0) { // Extended test value: 1E7.  Reduced to limit run time.
            dist.setMean(mean);
            double p = 0.1;
            double dp = p;
            while (p < .99) {
                double ret = Double.NaN;
                try {
                    ret = dist.inverseCumulativeProbability(p);
                    // Verify that returned value satisties definition
                    assertTrue(p >= dist.cumulativeProbability(ret));
                    assertTrue(p < dist.cumulativeProbability(ret + 1));
                } catch (MathException ex) {
                    fail("mean of " + mean + " and p of " + p + " caused " + ex.getMessage());
                }
                p += dp;
            }
            mean *= 10.0;
        }
    }
}

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